Theorem 3ad2antl1 1186

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antl1	|- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Proof of Theorem 3ad2antl1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ch ) -> th )
3	2	3adantl2 1181	1 |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1007

This theorem is referenced by:  acexmid  6049  f1oen4g  6991  f1dom4g  6992  ordiso2  7326  addlocpr  7851  distrlem1prl  7897  distrlem1pru  7898  ltsopr  7911  addcanprlemu  7930  fzo1fzo0n0  10522  pfxsuffeqwrdeq  11390  prodfap0  12231  prodfrecap  12232  muldvds2  12503  dvds2add  12511  dvds2sub  12512  dvdstr  12514  qusaddvallemg  13546  mulgnnsubcl  13851  mulgpropdg  13881  ringidss  14173  lmodprop2d  14496  cnpnei  15084  upxp  15137  lgsval4lem  15884  clwwlkccatlem  16395  clwwlkccat  16396